Volume interaction polymer segment

The first term refers to the mixing of the adsorbed layers, and the second to the elastic compression effect at distances less than one-layer thickness. K and K, are the volumes of polymer segment and solvent molecule respectively, n is the number of segments per polymer chain, F the number of chains per unit area of surface, x the Flory interaction parameter, and S , and are geometrical terms. 

Since the solvent molecules, the polymer segments, and the lattice sites are all assumed to be equal in volume, reaction (8.A) impUes constant volume conditions. Under these conditions, AU is needed and what we have called Aw might be better viewed as the contribution to the internal energy of a pairwise interaction AUp jj., where the subscript reminds us that this is the contribution of a single pair formation by reaction A. 

In an ensemble of flexible polymer chains, the instantaneous separation of two segments i and j varies from one molecule to another. Ensemble averages such as required in Eq. 2 are obtained by specifying W(r-jj), the probability that segments i and j are separated by ry. In an elastomeric rubber which is not so highly swollen that excluded volume interactions become important, and which is not too greatly deformed, W(r- j) takes a particularly simple form... 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

We now present results from molecular dynamics simulations in which all the chain monomers are coupled to a heat bath. The chains interact via the repiflsive portion of a shifted Lennard-Jones potential with a Lennard-Jones diameter a, which corresponds to a good solvent situation. For the bond potential between adjacent polymer segments we take a FENE (nonhnear bond) potential which gives an average nearest-neighbor monomer-monomer separation of typically a 0.97cr. In the simulation box with a volume LxL kLz there are 50 (if not stated otherwise) chains each of which consists of N -i-1... 

The size of a polymer molecule in solution is influenced by both the excluded volume effect and thermodynamic interactions between polymer segments and the solvent, so that in general =t= . The Flory (/S) expansion factor a is introduced to express this effect, by writing ... 

Here Vi and v are the partial specific volumes of the polymer (/ = 2,4) and the solvent, respectively M is the molar weight of the solvent and Xu and 724 are the Flory-Huggins interaction parameters, quantifying the energy of interaction between unlike lattice-based polymer segments (%24) or between polymer segments and solvent molecules (%u). 

Hoeve44,45) extended his theory further by considering not only interactions between the train segments but also interactions among the loops, and found that the latter lead to a decrease in the number of possible conformations of adsorbed polymer chains. He assumed that the segment density distribution in any loop is uniformly expanded in one dimension by a factor of at as a result of loop-loop interactions. The volume fraction of segments at a distance z > 6 is then given by... 

If the swelling behavior of carboxylated latexes could be characterized only by the increase in the volume fraction, i.e., in particle size, Eq. 1 would still hold but this is not the case in carboxylated latexes. The latex particles are swelled to a great extent, and the polymer segments are dissolved into the aqueous phase and interact between the particles by the hydrogen bonds and chain entanglements. Thus, Eq. 1 is not expected to hold at all and the interparticle interactions are expected to be dominant in the viscosity development of the latex. 

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