The journey of a thousand miles begins with a single step. I have been offering a course on molecular biophysics to advanced master level students since 1992 (the students have a background of physics, physical chemistry, chemical engineering, etc.). These students have little exposure to biology and organic chemistry. However, research focus is shifting towards soft matter science which is highly interdisciplinary, and holds a promise of generating customized, smart and biocompatible materials. Therefore, the need for learning physics of polymers and biopolymers has increased many folds. This course is taught with the objective to provide a robust background in these topics to students. I have converted my lecture notes into this publication. There are no textbooks in the market till date that cover the topics discussed herein in a single volume. The content has been used in a one semester course that I teach to MSc Physics students. The mathematical prerequisites for this book are modest.

Macromolecules in solutions can be distinctly characterized from their transport behaviour in the solution phase. The study of the transport processes yields coefficients like the diffusion coefficient, sedimentation coefficient, intrinsic viscosity, friction constant, etc. of the dissolved solute particles. These coefficients are dependent on two parameters. First is the size and shape of the solute particle. Second is the type of the solvent medium and its environment (pH, temperature, pressure, ionic strength, etc.).

Biophysics is not a single entity. It is a congregate of a plethora of disciplines such as molecular biology, physics, chemistry, biochemistry, bioinformatics, nanotechnology and even mathematics, to name a few. It answers a lot of questions quite similar to the ones researched in molecular biology but uses very unconventional methods to do so. To put it simply, it studies the interaction of various systems of a cell within the cell itself and outside it and can cover an astonishingly wide range of topics. More specifically, biophysics is the study of life phenomenon.

The living organism and the biosphere are not isolated; they exchange matter and energy continuously. From the thermodynamic perspective, “A living organism feeds on negative entropy”. Several alternative definitions exist. For example, the postulate of life states that “Life itself should be looked upon as a basic postulate of biology that does not lend itself to further analysis”. According to Bohr's uncertainty principle, “Physico-chemical properties of living organisms and the life phenomenon cannot be studied simultaneously”. This implies that cognition of one excludes the other. According to Schrödinger, “An organism is an aperiodic crystal”. This is a very well-defined conceptualization of any organism. An organism is a complex many-body system of numerous biomolecules interacting through innumerable physico-chemical reactions in an orderly, coordinated and regulated manner. In physical science, a crystal exhibits spatial order which allows a comprehensive description of this material through statistical means. However, no such order is observed in living organisms. Nonetheless, millions of biochemical reactions are carried out with excellent accuracy and reproducibility inside the numerous cells constituting the organism.

Settling down of heterogeneous suspensions over a period of time is a common phenomenon in everyday life. Such processes are very slow and completely governed by the uniform gravitational field of the earth. The importance of sedimentation as an analytic method to examine differential molecular weight of particles dispersed in a solvent medium was realized by Mason and Weaver (1924). The method was further developed into a novel branch of molecular transport theory by Svedberg (Svedberg and Pederson 1940). Determination of the molecular weight of synthetic polymers, proteins, nucleic acids and polysaccharides is of prime importance to both physical and organic chemists. Sedimentation methods have enjoyed remarkable popularity in analytic chemistry as reliable and robust tools. It must be realized that similar to molecular diffusion, sedimentation is a purely transport process. In fact, diffusion and sedimentation are competing processes in any given polymer–solvent system. Further any treatment of molecular transport in the dispersion medium, the flow equations are constituted following irreversible thermodynamic concepts. Thus, sedimentation equilibrium behaviour of polymer molecules in a solvent is significantly dependent on conformation, concentration, molecular weight and molecular charge density of the polymer. This makes the data interpretation of sedimentation experiments tedious. At the same time, one of the compelling reasons why the experiments to determine the molecular weight of proteins have been successful is because, for relatively homogeneous globular protein dispersions, the thermodynamic non-ideal terms are negligible and experimental data analysis is not cumbersome. In this chapter, some basic and essential features of sedimentation equilibrium will be discussed.

Basic concepts

Polymer solutions are complex liquids at any given temperature and require specialized thermodynamic treatment. The phase stability of polymer solutions is a pre-requisite for any potential application. In general, the theoretical calculation of the thermodynamic properties of liquids and solutions involves determination of their configurational properties (those that depend only on intermolecular interaction) ignoring the internal movement of molecules. As a result, we can define configurational or intermolecular energy of a solution as the energy of a liquid minus the energy of the same substance in the state of an ideal gas at the same temperature. Thus, as is evident, configurational thermodynamic properties can have combinatorial and/or non-combinatorial properties. This attribute of polymer solutions has attracted much attention in the past (Flory 1953; Hildebrand 1953; Huggins 1941, 1942).

Thermodynamics demands that entropy be the deciding factor that governs solution stability. Entropy of mixing arising due to the rearrangement of different molecules is called the geometrical or combinatorial entropy of mixing. The non-geometrical (non-combinatorial) contribution of the entropy of mixing results from the energy of interaction between the components present in the solution, resulting in contraction of the solvent and the formation of oriented solvation layers (hydration sheathes). This involves a decrease in entropy of the solvent. The former contribution(∆Scomb > 0) favours dissolution (∆G = ∆H – T∆S becomes more negative), the latter contribution (∆Snon-comb < 0) does not favour dissolution. We find that under specific conditions, in some systems, the first contribution may dominate over the second and then the total entropy of mixing becomes negative. This concept of polymer solutions has been discussed in excellent detail by Flory (1953).

Coacervation

Coacervation is usually defined as a process during which a homogenous solution of charged macromolecules, undergoes liquid–liquid phase separation, giving rise to a polyelectrolyte rich dense phase. It is the spontaneous formation of a dense liquid phase of poor solvent affinity. The loss of salvation arises from interaction of complementary macromolecular species. The formation of such fluids is well known in mixtures of complementary polyelectrolytes. It can also occur when mixing polyelectrolytes with colloidal particles.

Following the pioneering work of Bungenberg De Jong (1949), coacervates are either categorized as simple or complex based on the process that leads to coacervation. In simple coacervation, the addition of salt promotes coacervation. In complex coecarvation, oppositely charged polyelectrolytes can undergo coacervation through associative interactions. The other liquid phase, the supernatant, remains in equilibrium with the coacervate phase. These two liquid phases are immiscible and therefore, incompatible. Complex coacervation of polyelectrolytes can be achieved through electrostatic interaction with oppositely charged proteins and polymers. The charges on the polyelectrolytes must be large enough to cause significant electrostatic interactions, but not precipitation.

Potential applications of coacervates are many starting from protein purification, drug encapsulation to treatment of organic plumes. This calls for better understanding of the coacervate structure and the transport of biomolecules inside this phase. Several questions pertaining to the structure of coacervates can arise. The foremost of these is: is it a gel-like or a solution-like phase?

We have already discussed the global motion of long chain molecules in different thermodynamic and hydrodynamic environments. It has also been realized that in practice the probe length scale determines the physical parameter accessible in a measurement. In neutron scattering experiments, this is typically ~ a few nm, in X-ray scattering and diffraction techniques this is ~ 0.1–1 nm, electron microscopes use length scales of < 0.1 nm whereas for light scattering this is ~ 500 nm, for ultrasonics this is ~1 mm and classical gradient diffusion (CGD) uses probing length scales of several centimeters. The significance of these different measurement techniques is that if a polymer chain has a characteristic length of say ~100 nm, light scattering and CGD will measure its centre of mass translational diffusion, neutron scattering will probe its internal relaxation modes of segments and X-ray and electron microscopic techniques can be used to study the dynamics of the bond structures in individual monomers. On the other hand, if the chain has a physical dimension of ~ 1 μm, even light scattering can probe its internal modes. It must be realized that there is a whole class of polymer properties that involve mass transfer. Thus, the issue of polymer dynamics becomes relevant.

In this chapter, we shall be concerned with the dynamics of the internal modes in a long chain polymer. There are two different models for this—one is due to Rouse (1953) and the second one is due to Zimm (1956).

To get a clear idea of the phase state of matter it is necessary to understand the concept of phase. The term ‘phase’ can be defined structurally and thermodynamically. It is part of a system separated from other parts by interfaces and differing from them in thermodynamic properties. A phase must possess sufficient spatial extension for the concepts of pressure, temperature and other thermodynamic properties to be valid. Structurally, phases differ in the order of mutual arrangement of their molecules. Depending on this order, there are three phase states, namely: crystalline, liquid and gaseous.

Polymer substances possess high molecular mass and hence their boiling points must be very high. They decompose when heated, and their decomposition temperatures are always far below their boiling points. Due to this, polymeric substances cannot be converted to the gaseous state and exist only in the condensed state—liquid or solid. A study of the phase states and ordering of polymers reveals a number of specific features related to the large size of their molecules.

It is pertinent to discuss the possibility of formation of an ordered state in a polymer system. In any ordering process, the existence of short-range and long-range orders are defined by the distance over which the order extends, vis-a-vis, the dimensions of the monomers. A polymer is associated with two types of structural elements: monomers and chains. Hence, while discussing short-range or long-range order, it is informative to assign which of these elements is ordered. In practice, the existence of long-range order may comprise the arrangement of both structural elements. It is clear that long-range order of monomers in one dimension can generate a linear chain of polymers.